In the known pedal bicycle with auxiliary power means, the auxiliary power means is pivotally mounted on the bicycle frame and a friction wheel is installed at the end of the power output shaft of the auxiliary power means. The boosting effect is then achieved through the friction drive between the friction wheel and the bicycle tire when the wheel is rolling. However, for this kind of friction drive between the friction wheel and the tire, the change of air pressure within the tire often makes the transmission efficiency vary greatly. In particular, it is impossible to ensure the auxiliary power means to work at the rotating speed under the optimum operating condition since the wheel is driven directly by the auxiliary power means. As a result, the auxiliary power means consumes energy excessively. It becomes more obvious in particular when the auxiliary power means is a small gasoline engine. As for the case when clay and gravel are stacked on the tire, the friction transmission efficiency is affected further. The auxiliary power means even can't work normally. Also, a very complicated clutch-transmission and an operating device manipulating the clutch-transmission are used in the prior art for transferring the power from the auxiliary power means to the driving chain in order to boost the driving chain which is driven by the rider's pedaling. As the designed strength of the driving chain is defined according to the force of manpower pedaling, if on the driving chain a driving force is added besides, the chain will be overloaded. Hence, it is easy to be worn or broken. Moreover, in known bicycles using one driving chain, the structure of clutch-transmission is very complicated. Therefore, not only the possibility of failure becomes larger, particularly, the expensive price can't be accepted by the ordinary consumers.